Evolutionary Integral Equations and Applications

This text deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernals involved is that they consist of unbounded linear operations. The aim is a coherent presentation of the state-of-the-art of the theory including detailed proofs and its applications to problems from mathematical physics, such as viscoelasticity, heat conduction and electrodynamics with memory. The importance of evolutionary integral equations - which form a larger class than do evolution equations - stems from such applications and therefore special emphasis is placed on these. A number of models are derived and, by means of the developed theory, discussed thoroughly. An annotated bibliography containing 450 entries should prove the book’s value as a reference text.